Energy of Motion

Energy Definition: Energy can be defined as the capacity for doing work Work is done when a force moves an object over a given distance.

Forms of Energy The capacity for work, or energy, can come in many different forms. Examples of such forms are mechanical, electrical, chemical or nuclear energy.

Engineering Connection Understanding mechanical energy, or the energy of motion, is at the root of so many engineering applications in our world. Engineers design a wide range of consumer and industry devices — vehicles, appliances, computer hardware, factory equipment and even roller coasters — that use mechanical motion. To do this, they pay close attention to how energy is generated, stored and moved. Whether designing elevators, power plants or race cars, engineers take into consideration the concepts of work and power. Engineers collaborate to design dams that generate electricity from the flow of water. Part of this process involves calculations to determine how much power can be generated. Engineers incorporate what they know about momentum and collisions to design protective "crumple zones" and safety devices into vehicles to absorb most of the energy being transferred during a crash. In sports such as baseball and golf, investigating how the human body and equipment interacts with the ball during impact helps engineers design better and safer sports equipment. To reduce drag force and thus improve gas mileage, engineers design vehicles to be more aerodynamic. Engineers understand friction and use it to help control motion; some engineers design braking systems that prevent skidding. When designing vehicles — everything from push scooters to light rail trains to your car — engineers take into account all of the energy of motion concepts, because in real life, these forces are happening and interacting at the same time.

Key Words energy, motion, mechanical energy, kinetic energy, potential energy, work, power, waterwheel, momentum, conservation of momentum, conservation of energy, collision, elastic, inelastic, heat, friction

Kinetic and Potential Energy Engineering Connection: Engineers need to understand the many different forms of energy in order to design useful products Mechanical engineers are concerned about the mechanics of energy — how it is generated, stored and moved. Product design engineers apply the principles of potential and kinetic energy when they design consumer products. For example, a pencil sharpener employs mechanical energy and electrical energy. When designing a roller coaster, mechanical and civil engineers ensure that there is sufficient potential energy (which is converted to kinetic energy) to move the cars through the entire roller coaster ride.

Introduction

Mechanical Energy Definition: Energy that is composed of both potential energy and kinetic energy. Mechanical energy is the form of energy that is easiest to observe on a daily basis. All moving objects have mechanical energy. There are two types of mechanical energy: potential energy and kinetic energy.

Potential Energy Definition: The energy of position, or stored energy Potential energy is the energy that an object has because of its position and is measured in Joules (J). Potential energy can also be thought of as stored energy.

Kinetic Energy Definition: The energy of motion Kinetic energy is the energy an object has because of its motion and is also measured in Joules (J).

Conservation of Energy energy can change from one form into another. Due to the principle of conservation of energy, energy can change its form (potential, kinetic, heat/thermal, electrical, light, sound, etc.) but it is never created or destroyed.

Potential Energy potential energy is a result of an object's position, mass and the acceleration of gravity. A book resting on the edge of a table has potential energy; if you were to nudge it off the edge, the book would fall. It is sometimes called gravitational potential energy (PE).

Potential Energy Potential Energy can be expressed mathematically as follows: PE = mass x g x height or PE = weight x height PE is the potential energy g is the acceleration due to gravity At sea level, g = 9.81 meters/sec2 or 32.2 feet/sec2. In the metric system, we would commonly use mass in kilograms or grams with the first equation. With English units it is common to use weight in pounds with the second equation.

Kinetic Energy Kinetic energy (KE) is energy of motion. Any object that is moving has kinetic energy. An example is a baseball that has been thrown. The kinetic energy depends on both mass and velocity

Kinetic Energy Kinetic Energy can be expressed mathematically as follows: KE stands for kinetic energy. Note that a change in the velocity will have a much greater effect on the amount of kinetic energy because that term is squared. : :

Mechanical Energy The total amount of mechanical energy in a system is the sum of both potential and kinetic energy, also measured in Joules (J). Total Mechanical Energy = Potential Energy + Kinetic Energy

Swinging Pendulum This activity demonstrates how potential energy (PE) can be converted to kinetic energy (KE) and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by understanding conservation of energy and using the equations for PE and KE. The equations are justified as students experimentally measure the speed of the pendulum and compare theory with reality.

Engineering Connection Mechanical engineers design a wide range of consumer and industry devices — transportation vehicles, home appliances, computer hardware, factory equipment — that use mechanical motion. The design of equipment for demolition purposes is another example. Like the movement of a pendulum, when an enormous wrecking ball is held at a height, it possesses potential energy, and as it falls, its potential energy is converted to kinetic energy. As the wrecking ball makes contact with the structure to be destroyed, it transfers that energy to take down the structure.

Introduction Remember that an object's potential energy is due to its position (height) and an object's kinetic energy is due to its motion (velocity). Potential energy can be converted to kinetic energy by allowing the object to fall (for example, a roller coaster going down a big hill or a book falling off a shelf).

As a pendulum swings, its potential energy converts to kinetic and back to potential. Recall that energy may change its form, but there is no net change to the amount of energy. This is called conservation of energy.

Pre-lab Questions Where will the pendulum have the greatest potential energy? Where will it have the greatest kinetic energy? Will pendulums with higher heights go faster or slower?

Materials Materials List 2 stopwatches Masking tape 10 feet of string or fishing line Heavy object or weight Calculator

Three equations will be used in this activity: PE = m∙g∙h KE = ½ m∙Vt2 Vm = distance ÷ time where m is mass (kg), g is gravity (10 m/s2), h is height (meters), Vt is the calculated velocity (m/s), and Vm is the measure velocity (also m/s). To make the calculations simpler, use the metric system for measurements and calculations. This way, we can approximate gravity as 10 m/s2 and not worry about the English system's wacky units of mass.

Procedure Work in Groups of 4 Pick a height at which to release the pendulums. This should range from 15-40 cm (.15-.4 m) from the floor. Calculate the potential energy. Each team member should do this, as a way to verify the result. Calculate the theoretical velocity, Vt, at the bottom of the swing. Remember, KE at the bottom of the swing will equal PE at the top of the swing. Move to a designated area and tie your weight to the string/line so that it barely misses the ground while hanging. Place two pieces of tape on the wall on opposite sides of the hanging pendulum and record the distance between the two pieces. The distance should range from 30-50 cm (.3-.5m). Choose a larger distance for a higher height (i.e., h = 40 cm → distance = 50 cm). The pendulum should rest in the middle of the two pieces of tape. One person pull back the weight until it reaches one of the pieces of tape. Two team members synchronize two stopwatches, each holding one, and start timing when the pendulum is released. The first person stops his/her stopwatch when the pendulum passes over the opposite piece of tape and the second person stops his/her watch when it returns back to the initial piece of tape. Record both times and calculate the difference in time. Repeat the experiment four times so everyone can exchange roles. Complete the worksheet. How close were the values for the theoretical velocity and the measured velocity?

Questions to think about during the lab What happens to the potential energy as the pendulum swings down? When the pendulum swings to the other side, what happens to the kinetic energy?

Post Lab Discussion If engineers can use potential energy (height) of an object to calculate how fast it will travel when falling, can they do the reverse and calculate how high something will rise if they know its kinetic energy (velocity)? For what might an engineer use this information?

Activity Extensions So far, you have calculated the mechanical energy when it is either completely potential or kinetic energy. What about when the mechanical energy is composed of both? Create a table and/or graph showing the potential and kinetic energies of their pendulum at heights of 0, ¼h, ½h, ¾h, and h. (Hint: You already know the values at heights 0 [purely kinetic] and h [purely potential].)